We consider the reconstruction of a compactly supported source term in the constantcoefficient Helmholtz equation in R 3 , from the measurement of the outgoing solution at a source-enclosing sphere. The measurement is taken at a finite number of frequencies. We explicitly characterize certain finite-dimensional spaces of sources that can be stably reconstructed from such measurements. The characterization involves only the measurement frequencies and the problem geometry parameters. We derive a

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... singular value decomposition of the measurement operator, and prove a lower bound for the spectral bandwidth of this operator. By relating the singular value decomposition and the eigenvalue problem for the Dirichlet-Laplacian on the source support, we devise a fast and stable numerical method for the source reconstruction. We do numerical experiments to validate the stability and efficiency of the numerical method. * s153265@student.dtu.dk † mika@dtu.dk;note https://orcid.org/0000-0003-0038-9020 ‡ adrki@dtu.dk; https://orcid.org/0000-0003-2741-7423